Equivalence of 2 expressions involving radicals

Hi.

I need help in seeing how the following two expressions are equal.

and

I know they both evaluate to the same thing but I'm having a hard time seeing how they are related.
If someone could, perhaps through algebraic manipulation, show how one is equivalent to the other,
I would be immensely grateful.

I don't think it matters but the first arrived at by evaluating using a sum of angles
formula while the second is what you get if you decide to use a half angle formula.